Question

सिद्ध कीजिए कि
Cot^-1 x + cot^-1 y = cot^-1 {( xy-1)/(x+y)}

Answer 1

Question -

${cot}^{ - 1} x + cot {}^{ - 1} y = {cot}^{ - 1} ( \frac{xy - 1}{x + y} )$

solution :-

माना

${cot}^{ - 1} x = A$

तथा

${cot}^{ - 1} y = B$

तब x = cotA तथा y = cotB

हम जानते हैं कि,

$cot(A + B) = \frac{cotAcotB - 1}{cotA + cotB}$

$= \frac{xy - 1}{x + y} \\ \\ A + B = {cot}^{ - 1} \frac{xy - 1}{x + y} \\ \\ {cot}^{ - 1} x + {cot}^{ - 1} y = {cot }^{- 1} \frac{xy - 1}{x + y}$

Answer 2

Here is your answer........